Atkin-Lehner |
2+ 3- 7- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
85008w |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
114688 |
Modular degree for the optimal curve |
Δ |
-546106353408 = -1 · 28 · 32 · 7 · 112 · 234 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 11- -6 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,1836,19260] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:132:1] [54:528:1] |
Generators of the group modulo torsion |
j |
2672176941488/2133227943 |
j-invariant |
L |
11.998730142277 |
L(r)(E,1)/r! |
Ω |
0.59484299014988 |
Real period |
R |
5.0428139614955 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998126 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42504m1 |
Quadratic twists by: -4 |